The Evolution of Cosmological Theories: From Geocentric to Heliocentric Universe - Prof. B, Study notes of Physics

Download The Evolution of Cosmological Theories: From Geocentric to Heliocentric Universe - Prof. B and more Study notes Physics in PDF only on Docsity! Physics 1050 Concepts in Cosmology Class Notes and review for final August 24, 2009 Ancient Cosmic Systems Timeline 100,000 years ago- The Magic Universe Spirits activated everything 50,000 years ago- Anthropomorphic Universe Humans projected emotions into all things 10,000 years ago- The Mythic Universe Age of Theism, spirits = gods, primitive religions The Anthropocentric Universe Humans at cosmic center Astronomy’s great thinkers and the development of their theories… Aristotle o 4th Century B.C. (384-322 B.C.) o Student of Pluto at Academy o Developed his own philosophy o Established his own school: Lyceam o Theories accepted as method in Churches o Because we’re at the center of the universe, the earth is fixed in space and does not move. The Universe rotates around the world. o Everything on earth was the result of 4 things o Rest of universe was made up of a “5th Element” Terrestrial elements: Earth, air, water, fire Ether: “quintessence” >> unknown elements that made up the rest of the universe Terrestrial elements move up and down, ether elements move in perfect circles. Aristotle proposed that the earth was at the center of the universe, which was accepted as true during his time and well after. Most important part of Aristotle’s “ether” proposition is that the quintessent elements do not move up and down but rather in a circular motion. Aristotle’s Universe  It’s spatially finite  It’s a steady state  It’s perfect circular motions have no beginning or end  Long after Aristotle, religions tended to accept this theory Ptolemy o 2nd century A.D. (500 years after Aristotle) o Worked at Museum of Alexandria in Egypt o Astronomer and Mathematician o Pieced together the beginnings of modern astronomy Geocentric System: Theory concluded that sun, stars, moon don’t move in perfect circles Planets, stars, sun, moon, moved in epicycles For 1,300 years astronomers took this idea and attempted to improve it and even succeeded in making it look accurate. However, while it did seem to work, it was very wrong. Nicolaus Copernicus o 1473-1543 o Catholic Priest o Work: “Revolutions of the celestial spheres” o Work was published shortly before his death in 1543 o Proposed the sun, in fact, not the earth, was the center of the galaxy Heliocentric System  Proposed by Copernicus in his book  Earth, moon, planets revolve around the sun  Believe in perfect circular motion  Copernicus spent most of his life working on this theory in secrecy so as not to contradict religious belief, fearing he would be punished by the Church Tycho Brahe o 1546-1601 o Danish Astronomer o Wanted to avoid disputes with Churches and focus on accurate observations o Lead an “army” of astronomers Apparent Luminosity: L ____L0___ = L 4(Pi)r2 Temperature: Celsius Swedish Astronomer Temperature for water: 0O --------------------- 100O Freezing Boiling Fahrenheit German Astronomer Wanted 100 degrees to be the temperature of the human body Designed a system to make it work, but ended up having body at 98.6 Water Temperature 32O --------------------- 212O Freezing Boiling Kelvin = 273 + C Relationship between intrinsic luminosity and surface temperature of the sun Hertzspring-Russel (H-R diagram) Main Sequence Star- A star on the main sequence generates its energy by slowly converting hydrogen into helium The mass of the sun is 2 x 1033 grams The radius of the sun is 7x 1010 centimeters The Luminosity of the sun is 4 x 1033 (ergs per second) or 4 x 1020 megawats. Red Giant Stars Low temperature High Luminosity Very Large radius White Dwarf White because they’re extremely hot High luminosity Small radius Doppler Effect Christian Doppler- Austrian Physicist Discovered “Doppler” effect for sound in 1842 Discovered “Doppler” effect for light in 1848 Doppler Effect- When a source of sound or light are coming near a person, the waves have more “shrill” or a higher frequency than when they are going away from each other. Wavelength when going toward each other - short wavelength, high frequency Wavelength when source and receiver going away from each other - wavelength increases, frequency decreases. (lambda)= wavelengthλ (lambda)= wavelength Change in wavelength λ0 = relative speed Original wavelength λ speed of wave Change in frequency Frequency Δλ (lambda)= wavelength = v λ (lambda)= wavelength c Red Giants- Distended globes of gas with extremely large surface areas White Dwarfs- About the size of the earth, extremely dense and extremely hot dying stars. 10% of nearby stars are white dwarfs. Variable Stars: 25% are eclipsing binary system 75% are pulsating variables (expanding and contracting with a definite period) Capheids: Capheid variables: distance indicators First discovered in constellation Cepheus (where they get their name) Over 700 are known in the galaxy Period of 3-50 days, brightness can change by a factor of 5 Yellow Giants: 1912, Harriet Leavitt Discovered period-luminosity 3 ways to figure out how far away cosmic bodies are: 1) Stellar Parallax [apparent displacement or difference of orientation of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines] 2) L= Lo 4pi2 4) Period- luminosity Relation of caphoids 50,000 light years From sun to nucleus 30,000 light years Halo Globular Clusters: Population II stars Old (8-14 billion years old) Possibly no planets Poor in heavy elements Poor in gas and dust Open clusters Exist in the Disk Population I stars 100 or several hundred stars Pleiades Both clusters are important for distance measurements Plotted with HR diagrams. Uses apparent luminosity rather than intrinsic. MORE GALAXIES Dwarf elliptical: globular clusters, no bright center Giant Elliptical: spherical with bright nucleus CLUSTERS Coma Cluster- 450 million years from us, hundreds of stars Local Group- our galaxy and its closest neighbors, made up of 20 or so galaxies Super Clusters- clusters of many galaxies Our Galaxy is a member of the Virgo Super cluster Located within the constellation Virgo Thousands of galaxies Also known as the local Super cluster VOID RADIO GALAXIES, QSO’S, AGN’S AND MASSIVE BLACK HOLES Radio Galaxy- Usually giant elliptical galaxies that emit much more radio waves than they do optical. Radio wave energy comes from the synchrotron radiation of electrons Quasi Stellar Objects (quasars)- All star like objects of high red shift Extragalactic Far away Active Galactic Nucleus (AGN)- Far away galaxies with very active centers emitting jets and very bright light. Massive Black Holes- Astronomers have detected an extreme amount of stars, gas and clouds swirling around an unseen mass that is approximately 3 million solar masses. Because it cannot be detected, it is considered a black hole. Scientists now believe there is a black hole at the center of every galaxy in the universe. LARGE SCALE DISTRIBUTION OF MATTER (GALAXIES) IN THE UNIVERSE The universe was once believed to distribute galaxies like this: a center, surrounded by a “great wall” all located within a void. Now, after observation, it is believed that galaxies are distributed into a 3- dimensional grid with a cellular structure shaped like a honeycomb or a checkerboard. Galaxies exist on the “walls” or the lines that make up the checkerboard. In between these grids, where the checkerboard squares would be, exists a void. Galaxies MACHOS Massive Compact Halo Objects Very massive, very condensed areas of space located in the halos that at this point have yet been identified. THE BIG BANG THEORY We know that if the objects in space have red shift that they are moving away from us and away from each other. Using the principle of red shift, Edwin Hubble discovered that the universe is expanding. This opened the door for numbers of theories of what led to the expansion and what the origin of the universe really is. Hubble’s Findings: Speed of recession (how fast the galaxies are moving away) =EQUALS= A constant (known as Hubble Constant) times the galaxy’s distance from us Speed is determined by the Doppler effect Distance away is determined by speed of light Hubble Law: v = HR V= speed H= Hubble Constant R= distance Hubble described the expansion of the universe by using a balloon: Hubble Flow… NEWTON’S LAWS (1) If a free body is at rest, it will remain at rest and if it is moving, it will continue to move with the constant velocity on a straight line, unless acted upon by a force. [Law of intertia] (2) Rate of change (mv) with respect to time equals force a. Change in momentum = force Change in time (3) The force that an object has on another object equals the second object’s force on the first object. a. F1  change in P2 Change in time F2  Change in P1 Change in time Force of gravity- Universal attraction; every mass attracts every other mass. Fg= Gm1m2 R2 BLACK HOLES Kinetic energy = ½ mv2 Potential energy = GmM r To every mass “m” corresponds a radius. Gravitational radius = 2GM C2 Relativity theory Because gravity curves space and time, near an object, spacetime has a number of strange properties. There is a certain point of no return when approaching the gravitational pull of a black hole in which once you pass it, you can’t escape. This is a “black hole singularity” Singularity- Occurs when the laws of physics break down Gravitational Singularity- matter has collapsed to a singularity If it is covered by a horizon, it is a black hole singularity If it is not covered by a horizon, then it is known as a “naked” singularity. COSMOLOGICAL MODELS 2 absolute fundamentals Hubble expansion Cosmic Microwave Background radiation Newtonion Gravity M1 -------------------------- M2 R F= G1xM1xM2 r2 TOTAL ENERGY Energy of a galaxy = ½ mr2 (H 2 – 8 (pi) G (p)) 3 Penergy = C2 p-mass P-critical energy = 3 C 2 H 2 8 (pi) G (1) E = 0 p= 3 C 2 H 2 8 (pi) G (2) E < 0 p= 3 C 2 H 2 8 (pi) G (3) E > 0 p= 3 C 2 H 2 8 (pi) G 3 cases: (1) Energy = 0  Space is flat, 3-dimensional, universe expands forever (2) Energy < 0  Space is curved, positive curvature, volume is finite (3) Energy > 0  Space is curved, volume is infinite expands forever, curvature of space is negative Escape Velocity E > 0  Escape velocity of Earth: 11.2 km/sec Sun: 618 km/ sec Moon 2.38 km/sec Neutron star: 2x105 km/sec ACCELERATION OF THE UNIVERSE Cosmological Constant- Λ Repulsive force = 1/3 rΛ Efficient energy density = Λ ____ 4(pi) G Dark Energy- Defined to be a repulsive cosmic force. Energy density > 0 Pressure < 0 Unobservable, E=mc2 does not apply A cosmological constant Dark Energy makes up about 75% of the universe HOME WORK QUESTIONS AND ANSWERS 1. WHAT IS THE HUBBLE LAW? WHAT IS THE BIG BANG? Hubble law is the method in which Hubble used to calculate the rate at which the universe is expanding by the equation: v= Hr, with “v” as the valure for speed, “H” as the Hubble constant and “r” standing for distance. The Big Bang is the widely accepted theory of the origins of how the unverse began. It states the universe expanded from an extremely small, extremely dense point and then resulted in the creation of all matter observed in the universe today. The most concrete evidence for this theory is that it is mathematically proven that the universe is expanding and the it can be traced back all the way to a very small percentage of a second after the “explosion” occurred. 2. DESCRIBE THE HOMOGENEITY AND ISTROPY OF THE UNIVERSE Isotropy, which means that at any single point everything is the same when observed in all directions, and homogeneity, meaning that every point is the same, are two accepted ideas about the finite state of the universe. Given that the universe is homogeneous and isotropic, if one place is isotropic than all places are isotropic. And if space is isotropic at every point, than it is homogeneous. 3. DESCRIBE THE COSMIC MICROWAVE BACKGROUND RADIATION The CMBR represents the next fram of the big bang and is traveling uniformly in all directions. Temperature of the CMBR is approximately 3k and its wavelength is approximately 1 millimeter. There are 400 protons per cubic centimeter. 4. WHAT IS THE ESCAPE VELOCITY? Escape velocity is the speed at which the kinetic energy of an object is equal to its gravitational potential energy. It is required for any object to break free of a gravitational field and any speed less than this escape velocity would force the object back toward the surface emitting the gravitational pull. It is determined by the formula: 5. WHAT IS THE GRAVITATIONAL RADIUS OF AN ASTRONOMICAL BODY OF MASS M? The gravitational radius, or Schwarzchild radius, is a radius associated with every quantity of mass. For every mass, there a corresponding radius. If this radius contains a sufficient amount of mass and reaches a certain density, the force of gravity from the containted mass would be so great that no known force could prevent the mass from collapsing into a point of infinite density. The radius is determined by the formula: 2GM C2 6. IS THE UNIVERSE ACCELERATING? EXPLAIN. The universe is expanding at an increasing rate. Due to the amount of red shift witnessed in the universe and the constant change of distances between galaxies, which was discovered only about 10 years ago, it is considered to be accelerating. Due to what we know about gravity, it should be decelerating, however a force called “dark energy” causes the acceleration. 7. WHAT IS THE COSMOLOGICAL CONSTANT: .Λ The cosmological constant is a theory introduced by Einstein in his theory of relativity that is equivalent to a repulsive force that opposes the force of gravity. It was developed by Einstein to help explain his theory of a uniform universe. Adjusted so that it is possible to make the repulsion counter balance the gravity due to uniform distribution of matter, the cosmological constant is essentially “anti-gravity.” 8. WHAT IS THE PERCENTAGE OF C IS BELIEVED TO BE DUE TO…ρC IS BELIEVED TO BE DUE TO… Luminous Matter (known and observable): 5% Dark matter: 25% Dark Energy: 70% 9. EXPLAIN THE DEFINITION OF RED SHIFT “Z” IN TERMS OF RELATION 1 + Z = oλ (lambda)= wavelength λ (lambda)= wavelength Red shift is what occurs when emitted light moves away from the observer. Red shifted light has an increase in wavelength and decrease in frequency. Red shift is characterized by the relative difference between observed and emitted wavelength, referred to by the quantity “z.” Z = received – emittedλ (lambda)= wavelength λ (lambda)= wavelength emittedλ (lambda)= wavelength 10. EXPLAIN THE COSMOLOGICAL RED SHIFT Z USING THE RELATION: 1 + Z = Ro R As the universe expands, the wavelength of the originally emitted light expands as well. The rate of expansion of the universe (1+z) is equal to the current radius divided by the radius at the point of original wavelength ( )λ (lambda)= wavelength . 11. WHAT IS THE SIGNFICANCE OF Z = 0 & Z = INFINITY?